It has been known for a number of years that substantial modification of free and wall-bounded flows can be effected by the introduction of small disturbances at the flow boundary. These flows are inherently unstable and hence amplify small disturbances within a finite frequency bandwidth which depends critically on the flow conditions, especially velocity. The most amplified frequency is the frequency to which the flow is most unstable. This is the frequency at which these small disturbances grow the fastest. Under most conditions this frequency increases with the flow velocity. It has also been known that the stability characteristics of a given flow can be determined from (and depend upon) the spatial distributions of its means velocity. Deliberate forcing or excitation of the flow instabilities can lead to substantial alteration of the structure and evolution of the forced flow. In the absence of deliberate excitation, the unforced flow typically responds to small disturbances, i.e. background noise, already present in a given apparatus.
Free shear flows such as jets, wakes, or shear layers are dominated by the evolution of large scale coherent vertical structures, or eddies, resulting from the inherent flow instabilities. Although the nominal formation frequency of these vertical structures corresponds to the most unstable frequency of the flow in question, their appearance and global features in the unforced flow are normally irregular in space and time because of the random nature of the disturbances which trigger them. When a free shear flow is deliberately forced, the temporal and spatial evolution of the large vertical structures is substantially modified to include synchronization of the formation and passage frequency of the vertical structures to the excitation frequency and marked changes in their spatial growth and other global features. For some given flow conditions these changes depend, among other things, on the frequency and magnitude of the excitation.
There are numerous applications for utilizing deliberate forcing in a flow system. For example, the mixing of two fluids can be enhanced by inducing small flow fluctuations in adjoining boundaries of the fluids at or just prior to the fluids coming into contact. U.S. Pat. No. 4,257,224, granted Mar. 24, 1981, to I. Wygnanski and H. Fiedler for "METHOD AND APPARATUS FOR CONTROLLING THE MIXING OF TWO FLUIDS" discloses a variety of mechanical and electromechanical actuators for producing the desired boundary flow fluctuations. The apparatus there disclosed is reputed to be useful in improving the performance of combustors, flame holders and afterburners in turbojet engines as well as suppressing audible jet noise and increasing the output of ejector pumps and thrust augmenters.
Laboratory experiments have demonstrated that the most amplified frequency can be forced acoustically with a conventional speaker which also allows for tuning of the forcing signal when the flow conditions, such as velocity, change. Among the obvious disadvantages of speakers are their physical dimensions, weight, and power requirements. If the desired forcing frequency is known exactly, a piezoelectric actuator can be used for acoustic forcing. Among the reasons for the attractiveness of these devices are: (a) they are inherently very thin and lend themselves to surface mounting with little intrusion to fluid flow; (b) they can be fabricated in slabs of practically any planar dimensions, particularly in small sizes; (c) they can be arrayed as mosaics for mounting on nonplanar surfaces; (d) when operated at their resonance frequency, piezoelectric devices require relatively little electrical power for a considerable acoustical output; (e) they are temperature and corrosion resistant; and (f) many are available off the shelf at low cost. The obvious limitation of piezoelectric devices is that they operate efficiently only within a narrow frequency band around their resonance frequency, and hence should be replaced if the flow velocity is increased or decreased because of corresponding changes in the most amplified frequency.
One application in which piezoelectric actuators have found considerable usefulness is in fluidic control systems. Fluidics technology focuses on devices which utilize fluids to perform control and sending functions within larger and more complex mechanical systems. The operation of fluidic devices is typically based on interaction between an incoming main fluid jet and a number of control jets within a solid cavity of a large aspect ratio. The purpose of the control jets is to regulate the inlet flow between two or more outlets. The control jets are normally smaller jets of the same fluid and the control function is accomplished by their direct impingement on the main jet. The cavity of the fluidic device is normally not filled with the main jet fluid and plays a crucial role in the control of the main jet by acting essentially as a tuned resonator. Fluidic devices are of considerable engineering interest because they operate with fewer moving parts than comparable mechanical devices.
Fluidic devices in which the main fluid jet is acoustically manipulated by speakers or piezoelectric transducers are discussed in a review article by J. J. Kirshner and R. Gottron, entitled "FLUERICS 28: State of the Art 1969", Harry Diamond Laboratories Report HDL-TR-1478, December 1969. This article makes clear that the endplates of the cavity have a critical effect on the controllability of the main jet. Furthermore, unlike free jets, i.e. those well removed from solid boundaries, the main jet in fluidic devices is effectively controlled by a wall attachment mechanism. The authors comment that "a laminar jet is much more sensitive to certain frequencies that (sic.) to others", and when the main jet is acoustically forced, its "eddy-shedding characteristics" are altered.
The principles of acoustical forcing of a fluidic device are discussed in detail in an article by H. H. Unfried entitled "Experiment and Theory of Acoustically Controlled Fluid Switches", Proceedings of the Fluid Amplification Symposium Vol. II, Harry Diamond Laboratories, October 1965. This article clearly states that the successful operation of acoustically-controlled switching fluidic devices depends on the controllability of the main jet by the solid boundary, i.e. by attachment and detachment, and that "the stream operation takes place in the region of the flow where it is most sensitive to small disturbances" specified in terms of the Reynolds number and the Strouhal number, which, for a given fluid and geometry are dimensionless velocity and frequency, respectively. The article by Unifried also states that the operation of the fluidic device is significantly enhanced by coupling an acoustic resonator, essentially a tuned cavity, or a separation bubble, to the main jet. This cavity increases the frequency selectivity of the jet and should be tuned to a frequency for which the flow is most sensitive.
Acoustical forcing of fluidic devices by speakers or piezoelectric devices is also described in several United States patents. In U.S. Pat. No. 3,269,419, granted Aug. 30, 1966, to E. M. Dexter for "FLUID AMPLIFIERS", a laminar main jet, also referred to as a power jet, becomes turbulent by the indirect action of a piezoelectric crystal disposed in a sidewall of the flow chamber closely adjacent the jet boundary layer. The "mechanical motion of the crystal face 18 causes condensations and rarefactions of the air in its immediate vicinity and thereby causes a physical disruption in the boundary layer of the laminar power jet. In turn, the power jet becomes turbulent and its boundary layer diverges". According to Dexter, it is the interaction between the main jet and the side wall which causes the deflection of the main jet due to increased entrainment. It is clear that the cavity of the fluidic device plays a major role in the controllability of the main jet.
In U.S. Pat. No. 3,311,122 granted March 28, 1969, to R. N. Gottron for "ELECTRO-FLUID TRANSDUCER", the main (power) jet is manipulated indirectly by applying pressure perturbations through a conducting medium. These pressure perturbations are generated using various acoustic drivers and transducers including piezoelectric crystals. This patent discloses several arrangements in which the piezoelectric crystals are disposed in different positions in relation to the main jet.
Further refinement of these ideas are disclosed in U.S. Pat. No. 3,390,692 granted July 2, 1968, to E. G. Hastie and R. N. Gottron for "PNEUMATIC SIGNAL GENERATOR". In this patent, the inventors distinguish between two control methodologies for fluidic devices: (a) "stream interaction or momentum exchanges", and (b) a scheme "based on boundary layer control or the Coanda effect". In the former scheme the main jet is deflected by the control jets with the cavity side wall well removed, while in the latter scheme the geometry of the side walls is critical to the operation of the fluidic device. It is clear that both control schemes considered in this patent are greatly influenced by the presence of the two cavity end plates. In principle the two control schemes are similar because in each case a resonating cavity is formed between the main jet and the side walls which is excited acoustically. Acoustic excitation can result in substantial increase or decrease in the rate of entrainment of surrounding fluid by the main jet. Due to an increase in entrainment the jet deflects back to its original trajectory. The attachment, detachment, and reattachment of the main jet to the side walls is referred by as the "Coanda effect". This fluidic device employs one or more piezoelectric crystals for generating acoustical signals to deflect the main jet. Because the removal of the acoustic forcing results in deflection of the jet towards its original trajectory, the inventors propose to control the switching of the fluidic device by amplitude modulation of the signal which drives the piezoelectric crystal.
As noted above, the effect of excitation on the jet flow depends strongly on the frequency and the level or amplitude of the excitation input. In particular, variations of the excitation level at a given forcing frequency may lead to substantial variations in the response of the forced flow. Acoustical cavity excitation along the main jet results in the jet's deflection. The level of excitation determines the degree of deflection. It is clear that the continuous variation of the excitation level results in a gradual deflection of the main jet, while on/off switching of the excitation signal causes a flip/flop motion of the main jet. The Hastie, et. al. patent suggests that the level of the acoustic excitation may be regulated via amplitude modulation. Gradual variation of the excitation amplitude and hence gradual deflection of the main jet within the cavity may be achieved by sinusoidal variation or modulation of the excitation amplitude at frequencies which are lower than the forcing frequency. Switching action can be achieved by amplitude modulation using a square wave as modulating signal.
The piezoelectric flow manipulating devices described in the Dexter, Gottron and Hastie, et. al. patents share a common limitation, namely, a lack of versatility. For harmonic excitation at a given amplitude the largest displacement of a piezoelectric actuator occurs within a narrow frequency bandwidth around its resonance frequency. Furthermore, this bandwidth decreases with increasing resonance frequency. The piezoelectric actuator can be excited by a signal over a somewhat broader frequency ranges but more power is required the farther away the signal frequency is from the resonance frequency. For all practical purposes, each piezoelectric crystal must be excited at its own natural resonance frequency for efficient operation.
In the Dexter, Gottron and Hastie, et. al. patents the maximum efficient deflection of the power jet is achieved when the jet is subjected via an adjacent cavity or bubble to an excitation signal having a frequency with respect to which the jet flow is most unstable. When the excitation signal is applied at this frequency the disturbance is actually amplified in the fluid flow. What this means is that for these prior art devices to function properly the natural resonance frequency of the piezoelectric crystal must match or be very close to the most unstable frequency of the jet/cavity system. And it is known that the most unstable frequency of a fluid system varies with flow conditions such as geometry and velocity. Thus, any changes in the velocity of the flow through these prior devices over time would require replacement of the piezoelectric crystal with another crystal having a different resonance frequency matching the most unstable frequency of the system. Hence, the patented devices will function properly only within a limited range of power jet velocity.